Question

Satellite dishes are shaped like parabolas to optimally revive signals. The cross section of a satellite dish can be modeled by the function y= 1/8(x^2-4) where x and y are measured in feet. The x-axis represents the top of the opening dish.
Write a quadratic function that models the cross section of the satellite dish that is 6 feet wide and 1.5 deep.

Answer 1

The cross section of the satellite dish is an illustration of a quadratic function

The quadratic function that models the cross-section is y = 1/6(x^2 - 9)

How to determie the equation of the cross-section?

The given parameters are:

Width = 6 feet

Depth = 1.5 feet

Express the width the sum of two equal numbers

Width = 3 + 3

The above means that, the equation of the cross section passes through the x-axis at:

x = -3 and 3

So, we have:

y = a(x - 3) * (x + 3)

Express as the difference of two squares

y = a(x^2 - 9)

The depth is 1.5.

This is represented as: (x,y) =(0,-1.5)

So, we have:

-1.5 = a(0^2 - 9)

Evaluate the exponent

-1.5 = -9a

Divide both sides by -9

a = 1/6

Substitute 1/6 for a in y = a(x^2 - 9)

y = 1/6(x^2 - 9)

Hence, the quadratic function that models the cross-section is y = 1/6(x^2 - 9)

Read more about quadratic functions at:

brainly.com/question/1497716